I'm trying to find an inverse function of:
$$U(T) = \frac{R_2(T)}{R_1 + R_2(T)} \cdot U_1$$
where $R_2(T) = 1330 \cdot e^{3531.55 \cdot \left(\frac{1}{T + 273.15} - \frac{1}{279.75}\right)}$ and $R_1 = 1000$ and $U_1 = 5$.
I tried doing this by firstly expressing $R_2(T)$ in $U(T)$ in order to leave $U(T)$ only in terms of $U$ and $T$.
In the end, I obtain:
$$T(U) = \dfrac{1}{\dfrac{\ln{\frac{U - R_1}{1330 \cdot (U_1 - U)}}}{3531.55} + \dfrac{1}{295.75}} - 273.75.$$
Is this correct?